Accessing 100 GHz Mechanical Modes in Bulk Crystals at Cryogenic Temperatures

Abstract

Sub-terahertz electromechanics offers a promising route to probe mechanical quantum motion at experimentally friendly Kelvin temperatures. Traditionally, high-frequency mechanical resonators rely on advanced microfabrication to shape complex microstructures, while bulk crystals have been largely overlooked due to their large inertia and challenging transduction at such frequencies. Here we show that bulk lithium niobate can host mechanically accessible modes near 100 GHz when coupled via plug-and-play three-dimensional microwave cavities. This approach enables efficient, non-contact excitation of centimeter-scale, milligram-mass vibrational modes across 7.0--110 GHz, with mechanical quality factors up to 30,000 at W band. Furthermore, using a frequency-tunable superconducting niobium cavity at 4 K, we demonstrate strong coupling between a microwave cavity mode and multiple mechanical modes, enabling coherent energy exchange between microwave photons and mechanical phonons with cooperativity up to 16.6 at 110 GHz. These results establish a versatile platform for accessing massive high-frequency mechanical modes and for precision tests of mechanical quantum physics at elevated temperatures.

The paper asks whether bulk crystals can support accessible, low-loss mechanical modes near 100 GHz, where thermal occupation becomes small at Kelvin temperatures. It couples high-order thickness-shear modes of lithium niobate disks to three-dimensional microwave cavities through non-contact piezoelectric transduction. Aperture-based cavities concentrate the microwave field within the crystal; superconducting niobium cavities and dielectric-wire frequency tuning enable measurements of photon–phonon hybridization. Microwave reflection spectra resolve mechanical modes across 7–110 GHz, with estimated effective masses of 0.21–5.0 mg. Mode assignments are supported by regularly spaced resonances whose spacing agrees with the crystal thickness. Cryogenic mechanical quality factors reach approximately 30,000 in W band, with a highest reported $fQ$ product of $3.33\times10^{15}$ Hz. At approximately 85 and 110 GHz, tuning the cavity across successive mechanical resonances produces avoided crossings. Multimode input–output fits give coupling splittings $2g/(2\pi)$ of 17.08 and 36.24 MHz, respectively, exceeding the corresponding cavity and mechanical linewidths, with cooperativities of 12.28 and 16.60. Rotating the cavity also reveals two shear-polarization families with a 0.558% difference in free spectral range. The measurements establish linear spectral strong coupling, rather than nonclassical mechanical-state preparation or time-domain quantum-state transfer. At 110 GHz and 4.1 K, the inferred equilibrium thermal occupation is $\bar n\approx0.38$, but quantum-noise-limited thermometry is not demonstrated; the paper identifies suitable sub-THz quantum-limited amplifiers as a requirement. Cavity quality is reported to be limited by cryocooler cooling capacity, with improvement anticipated at lower temperature.